# Topic Archive: inner model theory

Set theory seminarFriday, December 12, 201412:00 pm

# Producing $M_n^{\#}$ from Boldface Level-wise Projective Determinacy

University of Münster

Projective determinacy is the statement that for certain infinite games, where the winning condition is projective, there is always a winning strategy for one of the two players. It has many nice consequences which are not decided by ZFC alone, e.g. that every projective set of reals is Lebesgue measurable. An old so far unpublished result by W. Hugh Woodin is that one can derive specific countable iterable models with Woodin cardinals, $M_n^{\#}$, from this assumption. Work by Itay Neeman shows the converse direction, i.e. projective determinacy is in fact equivalent to the existence of such models. These results connect the areas of inner model theory and descriptive set theory. We will give an overview of the relevant topics in both fields and, if time allows, sketch a proof of the result that for the odd levels of the projective hierarchy boldface $\Pi^1_{2n+1}$-determinacy implies the existence of $M_{2n}^{\#}(x)$ for all reals $x$.

Set theory seminarFriday, February 28, 201410:00 amGC 6417

# Covering, core model induction, and hod mice (Part II)

Rutgers University

We will discuss recent covering principles and show how they can be used to derive strength from failure of square.

Set theory seminarFriday, February 14, 201410:00 amGC6417

# Covering, core model induction and hod mice

Rutgers University

We will discuss recent covering principles and show how they can be used to derive strength from failure of square.

Rutgers University
Grigor Sargsyan is a professor of mathematics at Rutgers University. He received his Ph.D. at UC Berkeley, 2009. His research interests are in logic, set theory, and foundations: descriptive set theory, inner model theory, large cardinals, and forcing.